Welcome

Condensed matter sits at the crossroad between several fields of physics, such as quantum physics, equilibrium and out of equilibrium physics, quantum field theory, cold atomic gases and mesoscopic physics, among others.

In our group, we enjoy standing at those crossroads and to use these overlaps as efficiently as possible. To know more, go to the entries below or, even better, come to join forces.

Topics of current interest

Statistical mechanics and quantum fields on fractals

Fractals define a new realm to study basic phenomena in quantum field theory and statistical mechanics. This results from speci-

fic properties of fractals, e.g., their discrete scale invariance and the existence of distinct fractal dimensions each char­acterizing physical properties of fractals. We study different problems such as the conditions for Bose-Einstein condensation, superfluidity, phase transitions, thermo­dynamics of quantum radiation emitted by a fractal blackbody and quantum Einstein gravity.

Topology of tilings

The notion of tilings recover structures also known as quasicrystals, quasiperiodic and dynamical systems, symbolic dynamics, au­tomatic sequences among others. On perio-

dic structures, the Bloch theorem relates structural (Bragg structure) and spectral (band structure) aspects. Not on quasicrystals. On periodic structures, topo­­­logical invariants exist and are obtained from a Berry curvature. On quasi-periodic tilings, these tools are not available. We have been able to identify topological features, to calculate and to measure them.

Quantum phase transitions – Anomalies

Scale invariance is a property of our everyday environment. Its breaking gives rise to less common but beautiful structures like fractals.

At the quantum level, breaking of continuous scale invariance is a remarkable example of quantum phase transition also known as scale anomaly. We study the general features of this transition. In collaboration with exper­imentalists, we have shown evidence of this transition in Graphene. We also study other anomalies and critical properties of QED in (2+1) dimensions.

Statistical mechanics of out of equilibrium systems

The best understood systems in statistical mechanics are those at equilibrium (fixed energy) or in thermal contact with a thermostat. These systems are well descri-

bed by the Gibbs-Boltzmann probability to observe microscopic configurations. This breaks down far from equilibrium either in transient or stationary regimes. Recent approaches have improved near equilibrium linear app­rox­i­mations (e.g., exact models, macroscopic fluctuation theory). We extend these classical approaches and apply them to wave and quantum non equilibrium systems.

Cooperative effects and superradiance

Spontaneous emission of an atom coupled to quantum vacuum fluctuations is well un­derstood. When two or more atoms are bro-

ught together, they may cooperate in order to coherently enhance and modify their spontaneous emission. This paradigm is often known as super (or sub) radiance. In the presence of disorder (e.g., Anderson localization) these cooperative coherent effects are qualitatively modified and may even lead to a new type of phase transition (not Anderson localization), which we have proposed and actively study.